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Speculative suggestions are occasionally made about ways in which new physics experiments could hypothetically bring about a catastrophe leading to the end of life on Earth. Some of these hypothetical catastrophes, including the “killer strangelet” scenario considered in this paper, would also lead to the destruction of the planet and wider catastrophic consequences. In any case, the proposed catastrophe mechanisms generally rely on speculation about hypothetical phenomena for which there is no evidence, but which at first sight do not contradict the known laws of physics. Sometimes, such pessimistic hypotheses can be countered by arguments which show that the existence of the catastrophe mechanism is highly improbable, either because closer analysis shows that the proposed mechanism does in fact contradict well established physical principles, or because its existence would imply effects which we should almost certainly have observed but have not. Unfortunately, there is a difficulty in making an argument of this type sufficiently reassuring. One would like to be reassured that the chances of inadvertently triggering a global catastrophe are very small indeed before going ahead with an experiment. But finding arguments which justify this conclusion with the appropriate level of confidence may be very hard, if not impossible. Discouragingly few attempts to grapple with this issue have been made. In fact, even the obvious and fundamental question — how improbable does a catastrophe have to be to justify proceeding with an experiment? — seems never to have been seriously examined. The aim of this paper is to face this question squarely, in the hope of stimulating further debate. The particular stimulus for this paper was the debate over the safety of the RHIC supercollider experiments now underway at Brookhaven, and the ALICE experiments proposed by CERN. Speculation about possible disaster scenarios in these experiments led to some pressure for the experiments to be deferred or cancelled. In response, reports and papers were written that were used to justify commencing the RHIC experiments on the grounds that, inter alia, “Cosmic ray collisions provide ample reassurance that we are safe from a ... catastrophe at RHIC” [1] and “Beyond reasonable doubt, heavy-ion experiments at RHIC will not endanger our planet.” [2]. Here I will contend that the risk bounds obtained are actually not small, taking into account the scale of the catastrophe, either according to standard risk analysis or when compared with other adopted standards for acceptable risk to the public. Since the criteria used by Brookhaven to justify proceeding were developed by theoretical physicists and administrators, not by broader representatives of the public or by professionals in risk management, it seems desirable to bring these issues before a wider audience for the purposes of informed discussion and the formation of sounder public policy in future.

II. HISTORICAL EXAMPLES

The first catastrophe mechanism seriously considered seems to have been the possibility, raised in the 1940s at Los Alamos before the first atomic bomb tests, that fission or fusion bombs might ignite the atmosphere or oceans in an unstoppable chain reaction. Investigation led to an analysis by Konopinski et al. [3] which fairly definitively refuted the possibility. Compton was later reported, in a published interview [4] with Pearl Buck, as saying that he had decided not to proceed with the bomb tests if it were proved that the chances of global catastrophe were greater than three in a million, but that in the event calculation proved the figures slightly less. It is hard to understand how any meaningful calculation could have produced such a risk figure. The analysis of Ref. [3] gives convincing arguments against the possibility of a catastrophic chain reaction, based on well established physical principles. It concludes that it is unreasonable to expect a chain reaction propagated by nitrogen-nitrogen fusion reactions, and that an unlimited chain reaction consuming the atmosphere is less likely still. Other possible reactions, involving protons in clouds of steam liberated from the oceans, are also considered and argued to be less dangerous still. Konopinski et al. do note the “distant probability” that the mode of propagation of the reaction in the atmosphere might be more complicated than their analysis allows, in which case its conclusions might not apply, and they suggest that the complexity of their argument and the absence of a satisfactory experimental basis for it makes further work on the subject highly desirable. However, they offer nothing resembling a catastrophe risk estimate, nor any results from which a quantitative estimate could be derived. Yet, so far as I know, Compton never made an attempt to correct Buck’s account. Had she simply misunderstood, it would have been easy for Compton to disclaim the statement. And, had it not reflected his views, he would surely have wanted both to set the historical record straight and to defend his reputation against the charge of unwisely gambling with the future of humanity. The natural inference seems to be that Compton did indeed make the statement

2 reported.1 If so, although the risk figure itself appears unjustifiable, Compton presumably genuinely believed that an actual risk (not just a risk bound) of 3 × 10−6 of global catastrophe was roughly at the borderline of acceptability, in the cause of the American and allied effort to develop atomic weapons during World War Two. Apparently the figure did not worry 1959 American Weekly readers greatly, since no controversy ensued. It would be interesting to compare current opinion on the acceptability of a 3 × 10−6 risk of global catastrophe, in the circumstances of the Los Alamos project or otherwise. Another hypothetical catastrophe was examined some time ago by Hut and Rees [6,7]. They considered the possi- bility that the vacuum state we live in is not the true vacuum, but merely a local minimum of the effective potential. They asked whether, if this were the case, new generations of collider experiments could trigger a catastrophic tran- sition to the true vacuum, destroying not only the Earth but (eventually) all presently stable forms of matter in the cosmos. They showed that the probability of this occurring artificially in present or foreseeable collider experiments is considerably smaller than the probability of it having occurred naturally within our past light-cone.2 Most recently, in response to some (rather unfocussed) public concern [9], the possibility of some catastrophe arising from prospective experiments at the Brookhaven relativistic heavy ion collider (RHIC) was reviewed by Busza et al. (BJSW) and Dar et al. (DDH).3 Both groups paid most attention to the “killer strangelet” catastrophe scenario, which would arise if negatively charged metastable strange matter existed and could be produced in the experiments. As well as giving theoretical arguments against the hypotheses involved, both groups offer risk bounds inferred from empirical evidence. BJSW’s proposed bounds on the probability of catastrophe during the ten year lifetime of RHIC, derived from the survival of the Moon for 4.5 billion years, range from 10−5 to 2×10−11, depending on how conservative the assumptions made are [8]. DDH’s bounds, derived from the observed rate of supernovae, range from 2 × 10−6 (their pessimistic bound for a very slow catastrophe, in which the Earth is prematurely destroyed at some point in the billion years before it would anyway be consumed by the expanding Sun) to 2 × 10−8 (their main bound) [2]. As the quotations extracted in Section IV attest, both groups originally [1,2] suggested their empirical bounds alone were adequate to show that the experiments were safe. If correct, this conclusion would obviously be particularly welcome, since it would remove any need to evaluate the degree of confidence which should be placed in the theoretical arguments. The view that the empirical bounds were indeed adequate was also expressed in commentaries [12,13]. However, there are good reasons, explained below, to believe that this conclusion is incorrect, and indeed the claim was withdrawn by BJSW, after criticisms from the author of this paper. BJSW produced a second version of their preprint, removing the reassuring characterisations of their risk bounds and instead disavowing any attempt to decide what is an acceptable upper bound on pcatastrophe. In this revised version, BJSW also accept that the arguments for their empirically derived risk bounds could be invalidated if some additional pessimistic hypotheses were correct.4 BJSW’s revision of their preprint was an adequate response, from a purely scientific perspective. The public policy implications are troubling, however. My understanding is that the US government’s authorisation for the RHIC experiments to proceed was given partly on the basis of BJSW’s original arguments [1], whose discussions of risk were gravely flawed, as the quotations considered in Section IV illustrate. Public concern was countered by widely publicised [10,11] reassurances [12,13] that the risk was negligible, also relying heavily on the risk appraisals given in BJSW’s original preprint [1]. As far as I am aware, no effort was made by Brookhaven to reobtain authorisation on the basis of BJSW’s revised assessment, or to bring what is a significantly revised case to media and public attention.5 In my opinion, such efforts should have been made.

1In April 2000, in an attempt to understand this puzzling statement of Compton’s, I contacted Hans Bethe, a key figure in both the Los Alamos project and the theoretical work which led to the conclusion that the possibility of an atomic bomb explosion leading to global catastrophe was negligible. His view, relayed by an intermediary (Kurt Gottfried), was that the analysis of Konopinski et al. was definitive and does not allow one to make any meaningful statement about probabilities since − the conditions that must be met cannot be reached in any plausible manner. Bethe suggested that the 3 × 10 6 figure was made up by Compton “off the top of his head”, and is “far, far too large” [5]. 2These results are reviewed in Ref. [8]. Whether they offer adequate reassurance that no forseeable collider experiment will be unacceptably risky deserves reconsideration in the light of the arguments set out below. 3DDH also considered the ALICE experiments, scheduled to take place later at CERN. Their bounds on the risk of catastrophe ensuing from ALICE will not be considered here, though it is worth noting that even DDH regard them as inadequate and suggest further investigation. 4Some further possible loopholes in those arguments are listed in Ref. [14]. 5Indeed, the Brookhaven web pages continue, in April 2003, to direct readers to the original unamended version of BJSW’s preprint: see http://www.bnl.gov/rhic/docs/rhicreport.pdf.

3 It should be noted that BJSW stress [8] in the revised version of their paper that they regard the theoretical arguments alone as sufficiently compelling. This may be a defensible position, but it is not the case that was originally made and publicised.

III. SCOPE OF THIS PAPER

This paper is meant as a contribution to the debates over hypothetical catastrophe scenarios in the RHIC and ALICE collider experiments and over other hypothetical or real global catastrophe risks. It focusses on the key question: what risk of catastrophe could be acceptable? Other relevant questions are not considered. In particular, in the case of the collider experiments, no attempt is made to infer quantitative risk bounds from the qualitative theoretical arguments against the possibility of catastrophe, or to consider BJSW’s conclusion that the theoretical arguments alone offer sufficiently compelling reassurance [1,8]. The interest in this debate is not, of course, purely or mainly intellectual. The aim is to improve future policy over catastrophe risks. In particular, lessons can and should be learned from the evident flaws in BJSW’s and DDH’s discussions of risk. It is obviously unsatisfactory that the question of what constitutes an acceptable catastrophe risk should continue to be decided, in an ad hoc way, according to the personal risk criteria of scientists whom those in charge of experimental facilities choose to consult. Those criteria, however sincerely held and thoughtfully constructed, may be unrepresentative of general opinion or of expert opinion in risk analysis. Worse still, history suggests the risk criteria actually used may not be at all thoughtfully constructed. Compton’s reported opinion suggests, and the mischaracterisations of Refs. [1] and [2] illustrate very clearly, that scientists whose expertise is not in risk analysis or public policy cannot necessarily be relied on either to interpret the risk implications of the science correctly or to consider elementary arguments that tend to suggest more cautious risk criteria than can easily be satisfied. Relying on such inexpert appraisals is neither in the public interest nor the long term interests of science. Scientists and scientific institutions need to work to gain, maintain and justify public trust. Arguments which suggest that an experiment should proceed simply because the global catastrophe risk appears fairly low, without comparison to any pre-existing thresholds or guidelines, may not only fail to reassure, but may (not unreasonably) be interpreted as public relations exercises, intended to support a prejudged conclusion, rather than dispassionate scientific analyses. As Calogero notes [18], this has a long term cost for the credibility on questions of risk not only of those directly involved, but of all scientists, and the likely long term consequence is less informed and more irrational public debate and public policy. It may well not be possible to reach a complete consensus on firm guidelines. It seems unlikely, for instance, that some clear agreement will emerge that global catastrophe risks are small enough to be of negligible concern if and only if lower than, say, 10−20. Life is more complicated than that, and democratic debate more multi-faceted. Nonetheless — indeed, for this very reason — it would be valuable to have a spectrum of carefully argued opinion in the literature. I hope that the arguments below may spark further discussion.

IV. BJSW AND DDH’S RISK BOUNDS FOR THE “KILLER STRANGELET” SCENARIO

We turn now to the particulars of the catastrophe risk concerns raised over the RHIC and ALICE experiments, and specifically to the hypothetical “killer strangelet” catastrophe scenario analysed in some detail by BJSW and DDH. The “killer strangelet” scenario requires: (i) that stable strange matter exists, (ii) that a valley of stability exists for negatively charged strangelets, (iii) that negatively charged metastable strangelets could be produced in the ≈ 40 TeV Au-Au ion collisions planned at RHIC, (iv) that a strangelet so produced could survive collisions which bring it towards rest in surrounding matter, (v) that it would then fuse with nuclei, producing larger negatively charged strangelets, in a runaway reaction which eventually consumes the Earth.6 The theoretical arguments [8,2] against (i)-(iii) are generally regarded as convincing. If (i)-(iii) were nonetheless true, (iv) and (v) would also be plausible. If (i)-(v) were true, killer strangelets should also be produced in naturally occurring high energy heavy ion collisions, which take place when cosmic rays collide with one another or with heavy nuclei in celestial bodies. Naturally produced

6Aficionados of understatement may admire BJSW’s description: [1] “a catastrophic process with profound implications for health and safety”.

4 killer strangelets would be able to initiate runaway reactions capable of destroying asteroids, satellites such as the Moon, or stars. From the fact that the Moon has survived for 4.5 billion years, and from the fact that astronomical observations are not consistent with stars being converted into strange matter at any significant rate, bounds on the risk of catastrophe at RHIC can be derived [8,2]. Unfortunately, these derivations require assumptions about the types of interaction which produce strangelets, the velocity distribution of the strangelets produced, their interactions with nuclei, and their stability [8,2,14]. For this reason, BJSW and DDH give various bounds, derived by making more or less conservative assumptions. Even the weakest of these requires some assumptions [8,14]. Without knowing what level of confidence we can have in the relevant assumptions — a question which neither group addresses quantitatively — it is difficult to see how the bound figures can really be meaningful [14]. But even if the figures cannot really be justified, the comments made on them by BJSW, DDH and others give an interesting and valuable insight into the risk criteria of physicists and administrators involved in RHIC policy. −8 Assuming that RHIC runs for the scheduled 10 years, DDH obtain pcatastrophe < 2 × 10 for a fast catastrophic destruction of the Earth and p< 2 × 10−6 for a slow destruction that would be completed in the billion years before the Sun expands beyond Earth orbit. DDH describe these results as “a safe and stringent upper bound on the risk incurred in running [RHIC]”. They add that the two bounds respectively imply that “it is safe to run RHIC for 500 million years” and that “running the RHIC experiments for five million years is ... safe”. These last two statements are, of course, incorrect. DDH’s bounds, if valid, would establish only that it would be unlikely that the Earth would be destroyed very early in a RHIC experiment run over the relevant periods: the bounds are consistent with a high probability of destroying the Earth at some point during these hypothetically extended experiments.7 In the first version [1] of their paper, BJSW described DDH’s result as “a factor of 108 below the value required for the safety of RHIC”. This, of course, is also incorrect: a risk bound 108 times that of DDH’s would be consistent with a high probability of destroying the Earth within 5 years of the RHIC experiment — a risk level which even the most gung-ho physicist could hardly describe as “safety”. Using their own independent analyses, BJSW derive results that imply the following bounds from the survival of the Moon, given various assumptions (their Cases I-III) about −10 strangelet production, and again assuming that RHIC runs for the scheduled ten years: pcatastrophe <≈ 2 × 10 , −4 −5 pcatastrophe <≈ 10 , pcatastrophe <≈ 2 × 10 . They described the second and third of these cases as still leaving “a comfortable margin of error”. These comments, and that quoted at the start of this paragraph, are so obviously inapplicable — no sane person would seek to reassure the public by suggesting that a risk bound of 1 in ≈ 10000 of destroying the Earth represented a comfortable margin of error — that I suspect they must reflect some surprising confusion on BJSW’s part at the time of writing Ref. [1]. BJSW refined their calculations in the second version of their paper, extracting an extra factor of ten and producing −11 −5 bounds for a ten year run of the RHIC experiment of (Cases I-III): pcatastrophe <≈ 2 × 10 , pcatastrophe <≈ 10 , −6 pcatastrophe <≈ 2×10 . In this revised version, which followed criticisms of the comments noted above, no judgement is made as to whether any of the bounds are satisfactory. To quote BJSW: “We do not attempt to decide what is an acceptable upper limit on [pcatastrophe], nor do we attempt a ‘risk analysis’, weighing the probability of an adverse event against the severity of its consequences.” [8] We use the revised bounds in the following discussion, referring to them simply as BJSW’s bounds. −8 DDH’s main bound — pcatastrophe < 2×10 over the 10 year life of RHIC — has been widely referred to [1,2,13,12] in terms which suggest that it alone would be sufficiently reassuring to require no further analysis or risk optimisation. My impression is that many numerate and thoughtful people would disagree. My own reasons for doing so are given below.

V. RISK BOUNDS AND RISK ESTIMATES: AN IMPORTANT CAVEAT

It is important to stress that DDH’s and BJSW’s empirical arguments produce bounds on the risk of catastrophe, not estimates of that risk.8 Their bounds are based on the fact that we do not observe something that we should expect to observe if the risk were larger than some value p. A negative result of this form tells us nothing about the

7That these statements misrepresent their results was pointed out to DDH by the author in January 2000. 8In contrast, Compton’s reported statement on the risk of destroying life on Earth by a fission explosion is given in the form of a risk estimate — though, as noted above, it was not justifiable.

5 actual value of the risk. Everything in DDH’s and BJSW’s analyses is consistent with the true risk of catastrophe being zero — and if current theoretical understanding is correct, the risk is indeed precisely zero. When the destruction of the Earth is in question, though, it would be preferable not to have to rely on theoretical expectations alone. As Glashow and Wilson put it [13], “The word ‘unlikely’, however many times it is repeated, just isn’t enough to assuage our fears of this total disaster.” Hence the interest in looking at naturally occurring versions of the experiment, verifying that they have not resulted in catastrophes, and so producing firm bounds on the risk of catastrophe. Unfortunately, this approach has its pitfalls and limitations. Comparing the effects expected from hypothetical killer strangelets produced in naturally occurring heavy ion collisions and at RHIC is not completely straightforward. Theoretical assumptions need to be made in order to derive risk bounds. Unless we are very confident indeed in those assumptions, we cannot validly infer very small risk bounds this way [14,8]. And in any case, Nature may not necessarily have done versions of the experiment we are interested in often enough to produce sufficiently strong risk bounds. How do we begin to decide what constitutes a sufficiently strong risk bound? It seems to me that the correct approach in appraising risk bounds is to make worst case assumptions. So, if we are assured that pcatastrophe ≤ p0, and we have to decide whether that bound alone is sufficient reassurance, we have to ask whether we would be happy to proceed if we knew that pcatastrophe = p0. If not, then the bound alone is not sufficiently reassuring. Such a bound might still form part of a compelling case for the safety of an experiment if it could be combined with other arguments. For instance, in the case of RHIC, it might be argued that a combination of the theoretical arguments and empirical bounds is sufficiently reassuring, even if neither would be alone.9 I will not consider such arguments here. Nor — to reiterate — do I examine whether the theoretical arguments alone are sufficiently reassuring. The discussion below considers only the narrow question of whether the empirical bounds alone would suffice.

VI. RISK VERSUS EXPECTATION

The destruction of the Earth would entail the death of the ≈ 6 × 109 human population and of all other species, the loss of the historical record of the evolution of its biosphere, and the loss of almost all record of the culture developed by humanity.10 Added to these are the opportunity costs arising from the absence of future generations. Consider for the moment just the number of human deaths. If an experiment were expected to cause one human death, in the everyday use of the term — that is, it was likely that at least one person would die as a result of the experiment — its health and safety implications could not be said to be negligible. Now, when we are dealing with small risks of large catastrophes, we cannot directly use this measure: an experiment with small risk is expected to cause no human deaths, in the sense that this is the likeliest outcome. However, we can calculate a related measure: the statistical expectation value of the number of human deaths. The expectation value of the number of human 9 deaths ensuing from an Earth-destroying catastrophe is Ed = pcatastropheN, where N ≈ 6 × 10 is the current human population. So, if we accept Ed as an appropriate measure of the seriousness of a risk — and the next section explains why we should — then any risk that does not satisfy

−10 pcatastrophe ≪ 1.6 × 10 (1) is not negligible. Of the bounds above, neither of DDH’s ensure that (1) is satisfied, nor do the second and third of BJSW’s. BJSW’s least conservative lunar survival bound (Case I) comes closer, but still fails unless a factor of 1/8 — i.e. in this case a probability of 1/8 of causing one human death — is regarded as negligible.

9Arguments along these lines have been suggested in informal discussions, but to the best of my knowledge none has been set out in print. Such an argument would need to be made very carefully, since the theoretical arguments and empirical bounds are not independent. As already noted, the empirical bounds still rely on theoretical assumptions, and if theoretical expectations were incorrect, the derivation of the empirical bounds might also be affected. 10A few spacecraft, including the message-bearing Pioneer and Voyager craft, would survive, as would the – continually attenuating – electromagnetic signals generated on Earth.

6 Making the comparison in terms of expectations, DDH’s main (tighter) bound implies that the expectation value of the number of human fatalities caused by RHIC over ten years will not exceed 120. Put this way, this bound seems far from adequately reassuring.

VII. IS THE EXPECTATION VALUE OF THE NUMBER OF FATALITIES RELEVANT?

It might perhaps be argued that the preceding calculation is misleading. After all, DDH’s bounds on pcatastrophe represent probabilities small enough to be negligible in most circumstances. Most of us take 2 × 10−8 risks of death in our stride: the risk of a typical US citizen dying in a shark attack in any given year is comparable. Translating the bound value into Ed, the expected number of fatalities, makes it seem significant. But is it really reasonable to use expected fatalities as a measure of the safety of a risk bound? Actually, the next section argues that considering Ed alone still greatly underestimates the cost. But first let us consider whether requiring Ed < 1 gives a sensible upper bound on negligible risk, assuming that it is agreed that the certainty of causing one death would not be negligible. I believe most expert opinion would agree that it does, for the following reasons. First, everyone agrees that in carrying out any risk analysis we need the cost or utility of the various outcomes, not merely their probability: a 10−3 chance of losing one dollar is better than a 10−3 chance of losing one million dollars, and so on. Second, a fundamental principle of risk analysis is that in normal circumstances rational people are risk averse. If X represents a random process whose possible outcomes xi have probabilities pi, and if V (xi) represents the value to the community of outcome xi, then the value V (X) of a single run of X — that is, the value of allowing precisely one of the xi to happen, with respective chances pi — is generally assumed to obey

V (X) ≤ X piV (xi) . (2) i

The values of undesirable outcomes, of course, are negative: we refer to −V (xi) as the cost of xi. A second principle is that the utility or cost function is concave. Applied to the cost of a loss of human lives, this implies that the cost to society of N deaths is at least N times as great as the cost of 1 death: if xN and x1 represent the two events, then

V (xN ) ≤ NV (x1) (3)

The principles of risk aversion and concave utility explain, for example, why it can often be rational to take out insurance, even though on average the insurance company expects to make a profit and the customer a loss. Similarly, it explains why investors almost universally require investments that involve higher risk to offer a higher expected profit in compensation. By considering a random process X with probability 2 × 10−8 of killing 6 × 109 people and probability (1 − 2 × 10−8) of killing no one, we see these principles together imply that a 2 × 10−8 chance of killing 6 × 109 people is at least as bad as the certainty of killing 120 people. In summary, to demonstrate that the risk is negligible, we would need to show that Ed is considerably smaller than one — precisely how much smaller depending on precisely how risk averse one is when it comes to global catastrophe. Neither DDH’s nor BJSW’s bounds satisfy this criterion. To speak of the bounds being “safe and stringent” or guaranteeing “comfortable margins of error” is, on this analysis, simply incorrect. Similarly, to demonstrate that the risk is acceptable, it would be necessary (though not necessarily sufficient) to show that Ed is small enough that the certainty of the experiment killing Ed people would be acceptable. Put another way, if it would be unacceptable for the experiment to lead to the certain loss of Ed lives, then a risk at the bound value would be unacceptable. Suppose, counterfactually, that we knew that the RHIC experiment were certain to kill precisely N people (and no more). What value of N would be acceptable? Answers will vary, but my guess is that most would be somewhere in the range < 10 or so. In particular, I think it clear that RHIC would not have obtained political authorisation if it was thought certain to kill precisely 120 people: that would be regarded as an unacceptably high cost. From the discussion of this section, it follows that a global catastrophe risk at the DDH bound value would be at least as unacceptable. Although the observations made in this section are elementary, it is worth noting that the CERN panel did not acknowledge their validity. The response of Alvaro de Rujula, the panel leader, is accurately summarised by his opinion, quoted in New Scientist [15], that it is “absurd” to take the risk bound probability and multiply it by the global population. I recommend contemplation of this comment to anyone inclined to automatic faith in the risk analysis expertise of scientists chosen by institutions to argue for the safety of their experiments.

7 VIII. COMPARISON WITH EXISTING RISK POLICIES

DDH’s and BJSW’s risk bounds were presented and discussed by DDH [2] and BJSW [1], in a statement by John Marburger, then director of Brookhaven [12], and in a commentary by Glashow and Wilson [13]. None of these discussions make comparisons with risk criteria or optimisation procedures applied to other potentially hazardous activities. This is unfortunate, since risk comparisons are generally illuminating, and in this case suggest that regarding the risk bounds per se as adequate would be wildly inconsistent with at least some established policy. For example, the UK National Radiological Protection Board requires that the risk of serious deleterious health effects arising from a nuclear solid waste disposal facility must always be bounded at below 10−5 per year, that risk optimisation procedures should be continued until the risk is below 10−6 per year, and that the risk of low probability natural events which could lead to serious deterministic health effects should be separately bounded at 10−6 per year [16]. The risk figures apply to the critical group of individuals, typically numbering between a few and a few hundred, whose habits or location render them most at risk. Quite typically, the events whose risk is bounded would be expected to kill fewer than 10 people. In summary, according to established policy for these radiation hazards, it is not acceptable to incur a risk of greater than 10−6 per year of killing ≈ 5 people. The risk aversion arguments of the last section suggest that a consistent policy on catastrophe risk should treat a risk greater than 10−15 per year of killing the global population as even less acceptable. An acceptable risk bound should thus imply

−15 pcatastrophe ≪ 10 per year . (4)

IX. FUTURE LIVES

The discussion so far has considered only the expected cost due to immediate human fatalities, neglecting the other costs mentioned earlier. These are very hard to quantify in any commensurable way. (What is the value of the rest of the biosphere compared to that of the human population? What price do we put on the historical record?) However, it is, at least arguably, possible to assign a sensible and commensurable value to one of these further costs — the loss of future generations — by estimating the number of future human lives which would not take place if the planet were destroyed in the near future. This line of argument cannot be followed without addressing two rather complex questions: Should we value our successors’ lives as highly as those of our contemporaries? And can we say anything meaningful about the likely fate of humanity over the billion years of life the Earth has left (or beyond)? To the first, my own answer is “yes”, partly because I cannot see any good reason to prefer an unknown contemporary to an unknown successor, and partly because it seems to me our lives have value in the first place largely because they form part of ongoing human history. This view finds some support in established policy: the UK National Radiological Protection Board guidlines cited above also explicitly state that those living at any time in the future should be given a level of protection at least equivalent to that given to those alive now. As for futurology, there are obviously so many unknowns that attempting detailed analysis seems pointless. I offer only a crude calculation, which is obviously open to criticism, but at least suggests a starting point for discussion. Suppose, optimistically, that humanity has a reasonable chance of surviving (in some form) for the lifetime of the Earth. Suppose also that there is a reasonable chance of arranging things so that the sum global quality of life is at least at the level of today, and the global population is roughly today’s: 1010 in round figures. And suppose we neglect the possibility that the human lifespan may increase beyond 102, on the grounds that it is arguably irrelevant: arguably, one can make a reasonable approximation — reasonable, that is, given the uncertainties in the entire discussion — by considering the total number of person-years, so that for instance a 700-year life is equated to seven 100-year lives. Let us also, conservatively, neglect the effect of migration to other planets some time in the future, which would presumably (i) allow the human population to vastly increase over the next billion years and (ii) permit humanity to survive beyond a billion years. The cost of the destruction of the Earth today would then be roughly 101010−2109 = 1017 lives, or 107 greater than the cost earlier calculated. Including this factor in the earlier calculation derived from the NRPB’s risk bounds would mean that an acceptable risk bound should imply

−22 pcatastrophe ≪ 10 per year . (5)

8 This further proposed tightening of risk bounds is controversial in all sorts of ways. To mention just one: regarding the loss of future lives as a separate cost raises the question — a cost to whom? To those potential future generations, deprived of the possibility of existence? To us, deprived of descendants and successors? Both, I think — but I concede that both lines of thought raise some difficulties. Another way of approaching the question is to ask a different hypothetical question: would it be far worse if all of us (or all life on Earth) were killed than if almost all of us (or almost all life on Earth) were, supposing that in the second case the planet remained otherwise fit for life? Answering “yes” suggests placing a high relative value on future lives, since the number of immediate fatalities is almost the same in both cases. Those who answer “no” will presumably not find any of the arguments of this section convincing. My impression is that the question has not been widely enough debated for it to be possible to say which view (if either) reflects general opinion. For the moment, then, whichever view one holds on future lives, it is worth bearing in mind that the majority view, on which catastrophe risk policy should properly be based, may turn out to differ.

X. SOME COUNTERARGUMENTS

Calculations and comparisons are indispensable in rationalising risk policy and in highlighting inconsistencies. However, there is no generally agreed set of principles from which we can decide policy in every instance. Politics do not form a subset of mathematics. The above arguments could well be opposed on many different grounds. I consider here some counterarguments which have been suggested to me in discussions.

• One obvious criticism is that the arguments above consider the cost of a catastrophe risk but not the benefits gained by taking the risk. For that reason, it may be argued, they are bound to produce over-cautious prescrip- tions. After all, no risk at all is worth taking unless there is some benefit. Without a cost-benefit analysis, no sensible conclusion can be reached. This is a partially fair criticism, but only partially. It should be stressed that it does not apply to the argument of section VI, since using the number of deaths as a measure of safety is justified by comparing the implicit cost-benefit tradeoffs in conclusions that would be generally agreed. It seems to me pretty uncontroversial that, despite the benefits of RHIC, the experiment would not be allowed to proceed if it were certain (say, because of some radiation hazard) to cause precisely 120 deaths among the population at large. If that is accepted, it follows that a risk at the DDH bound value would be unacceptably high, even when the benefits of RHIC were taken into account. −15 That said, some forms of cost-benefit analysis might indeed suggest that requiring pcatastrophe ≪ 10 per year or lower may be over-stringent. The likely immediate benefit of the RHIC experiments — advancing our understanding of basic science — is not negligible. Moreover, the possible benefits presumably include at least some probability — perhaps small, but not necessarily small compared to 10−15 — of contributing in some presently unforeseen way to a discovery with a very large beneficial impact on future human lives. The foresight problem is particularly acute here, of course, since one can also imagine low probability outcomes, other than the catastrophe scenario, with a large negative impact. But, if one takes the view that scientific and technological progress have on balance been beneficial and are likely to continue to be, the small possibility of a benefit that would save (or enable) many future human lives gives, at least in principle, something to offset against the small possibility of a catastrophe. It is important to be clear, though, that by definition no cost-benefit argument could justify a claim that the risks involved are negligible. Rather, it would make the case for proceeding with RHIC by suggesting that the risks, though possibly not negligible, were justified by the benefits. This is not the case which has been made. Such a case might or might not be widely accepted. • It may be argued that the more stringent risk criteria suggested above for global catastrophe, even if rationally justifiable in theory, are impossibly Utopian. If we took them seriously, and attempted to ensure that they were satisfied before proceeding with any enterprise, we would stop, not only collider experiments, but many other human activities. Progress would become impossible; life might be made unliveable. Maybe — but I would be cautious about accepting this sort of defeatism too readily. We begin from a state where risk bounds of 10−6 are used quite widely, for instance in the solid nuclear waste disposal guidelines cited above. It does not seem obvious to me that, with careful attention to the problems, we could not ensure that catastrophe risks associated to specific mechanisms are many further orders of magnitude smaller. On the

9 contrary, it seems quite clear that in some cases catastrophe risk bounds could be substantially reduced. The RHIC experiments are an excellent example: had the problem of reducing the risk bounds been taken seriously, further theoretical research, perhaps combined with a tentative experimental programme aimed at carefully testing our understanding of the new physics involved before running the full experiment, could almost certainly have reduced the bounds very significantly. Of course, this is not to say that risk avoidance is cost free. One has to accept that more stringent catastrophe risk criteria might indeed delay or preclude at least some interesting future experiments. It seems to me we just have to accept this as a fact of life. One cannot defensibly adopt a mindset which requires that every interesting experiment must be carried out, and that sees every risk analysis as an exercise in justifying this foregone conclusion. Human life, collectively as well as individually, is, after all, fragile. Our understanding of nature is limited, and there are surely many dangers we have not yet appreciated. Due caution is appropriate. We should not, in any case, rely on speculation about the implications of a more cautious catastrophe risk policy. If it were to become clear that it would be effectively impossible to apply a policy on catastrophe risks consistently, obviously that policy would need to be reconsidered. Unless and until carefully justified arguments are made, identifying specific examples of problematic catastrophe risks, it seems premature to worry. • The justifications given above for risk criteria may strike some as a bad policy guide, since they assume that preserving human lives is in some sense a primary value against which our actions should be judged. Actually, of course, we are guided by many other values. Few people consistently act so as to maximise their own life expectation, for example: many risky pleasures are widely indulged in. Perhaps we should accept that what applies to us as individuals applies also to us as a species: worrying about very small risks detracts too much from the quality of our existence to be the best course. This is certainly arguable. On the other hand, current risk policy tends to count the cost in human lives for a good reason: because that particular value seems to be more widely shared and more strongly held than most. It cannot possibly adequately represent the variety of individual values we bring to any policy debate, but it is a measure which, by general consensus, is very important. Making a generally acceptable policy for extinction risks on some other basis would require establishing a fairly firm consensus on what that basis should be. No such consensus seems to exist at the moment. • There is what might be termed the argument of dominant risk. We face many other extinction risks, some natural (large asteroid impact), some wholly or partly self-created (global nuclear war, catastrophic extinction of species as a result of human impact on the global ecosystem, catastrophic climate change as a result of human impact on the global environment). There is a view which suggests that a new artificial risk is acceptable if it is smaller than existing risks. A refinement of this view is that a new artificial risk is acceptable only if smaller than presently unavoidable natural risks. In two further common variants of these two views, “smaller than” is replaced by “very small compared to”. Large asteroid impact seems to be the greatest known natural extinction risk that can be reasonably well estimated. The risk of the Earth being hit by an asteroid of diameter 10 km is estimated to be 10−8 per year [17]. Such an impact would be so devastating that it is generally thought very likely that it would cause mass extinctions of species, and very plausible that we would be among the species extinguished. Accepting that last hypothesis, perhaps at the price of another order of magnitude, gives an estimate of 10−8-10−9 per year for this natural extinction risk. Following the argument of dominant risk leads to the so-called “asteroid test”, according to which an artificial extinction risk is acceptable if smaller than ≈ 10−9 per year, or in the more conservative version, very small compared to 10−9 per year.11 My impression from discussions is that many thoughtful people find some version of the argument of dominant risk reasonable, but that many equally thoughtful people find this line of argument entirely irrational. My sympathies are with the latter. Why should the existence of one risk, which may be distressingly high, justify taking another easily avoidable risk, which, even if much lower, may still be unacceptably high? Unavoidable natural risks are not normally believed to justify wilfully inflicting avoidable risks on third parties. Everyone

11Versions of the “asteroid test” have been discussed as possible justifications for the acceptability of the BJSW and DDH risk bounds by several people involved in policy formation at CERN and Brookhaven: for example in W. Pratt et al., Brookhaven National Laboratory Memo to T. Ludlam and J. Marburger, 17.2.00. The test is also considered in Ref. [18].

10 now living is very likely to die within the next 120 years, and would be very likely to die of natural causes in that timespan even if exposed to no other risks. An industry which added slightly to the natural risk level, annually killing 10000 people who had made no choice to accept the extra risk, would not find much sympathy for the defense that these extra deaths were more or less lost in the noise compared to natural wastage. A further problem specific to the asteroid test is that it assumes that asteroid extinction risks are either unavoidable or else, though avoidable in principle, small enough to be tolerable. In fact, the asteroid threat is not unavoidable with current and foreseeable technology, and passive and active counter-measures are being seriously considered. That said, let me reiterate that many people seem to be persuaded by some version of the argument of dominant risk. It no doubt deserves a more careful discussion than is given here. The above brief sketch of a counterar- gument is not meant to dismiss the “asteroid test” and related criteria out of hand, but rather just to note that there are serious counterarguments. I do not believe these criteria represent anything approaching a consensus view. Unless and until it becomes clear that they do, they cannot legitimately be used to justify catastrophe risks.

XI. FINAL COMMENT

The particular artificial extinction risk considered in this paper is hypothetical, and there are good arguments to suggest that the actual risk is small or zero. But, as already noted, we face other undoubtedly real and not necessarily small artificial extinction risks. The arguments above, which suggest that the true costs of extinction are generally underestimated, obviously apply generally. For instance, while the serious costs associated with artificially induced global warming are widely (albeit not widely enough) appreciated, the extra cost associated with the small risk of a truly catastrophic climate change does not seem to have been much considered. Yet it might be that, with proper accounting, the cost of the risk of climatic catastrophe would be the greater. Similarly, although some (insufficient) attention is being paid to the costs associated with the loss of biodiversity caused by human impact on the environment, the cost of the risk of a catastrophic collapse of the global ecosystem seems to have been generally neglected. In these and other areas where modelling is possible, the arguments above suggest we should encourage and pay attention to research into unlikely but not inconceivable catastrophic outcomes, and try to quantify the risk they represent, rather than focussing only on likelier outcomes which may be very deleterious but are not truly catastrophic. Acknowledgements Many friends, colleagues and experts in other fields have taken considerable time and trouble to help with the preparation of this article. I would particularly like to thank Clark Chapman for a great deal of helpful advice on scientific and risk policy questions and for many helpful suggestions. I am also very grateful to Andy Baker, for supplying references on risk assessments for nuclear waste storage; Hans Bethe and Kurt Gottfried, for clarifications of the history of work at Los Alamos on the atmospheric and oceanic ignition problems; Guido Altarelli, John Ellis, Jean-Pierre Revol, Jurgen Schukraft and Gavin Salam for suggesting relevant questions; Conor Houghton and Katinka Ridderbos for very helpful criticisms; Richard Binzel, Hans Rickman and David Morrison for helpful explanations of the risks associated with meteor impact and of research on public perception of risk; Holger Bech Nielsen, for several interesting discussions on collider risks; Francesco Calogero, for helpful discussions and criticisms and for kindly supplying a draft copy of Ref. [18]. It is also a pleasure to thank Stephen Adler, Michael Atiyah, Guido Bacciagaluppi, David Bailin, Jon Barrett, John Barrow, Dorothy Bishop, James Blodgett, Charlotte Bonardi, Harvey Brown, Jeremy Butterfield, Joanne Cohn, Jane Cox, Ian Crotty, Matthias D¨orrzapf, Fay Dowker, Ian Drummond, Michael Froomkin, Nicolas Gisin, Peter Goddard, Stephen Gratton, Lucien Hardy, Julia Hawkins, Ron Horgan, Tobias Hurth, Simon Judge, Anjali Kumar, Peter Landshoff, Nathan Lepora, Karen McDonald, Jane MacGibbon, David Mermin, Hugh Osborn, Sandu Popescu, Patrick Rabbitt, Martin Rees, Stefan Reimoser, Peter Ruback, Paul Saffin, Hugh Shanahan, Graham Shore, Tony Sudbery, John Taylor, Daniel Waldram, Peter West and Toby Wiseman for helpful discussions or correspondence. I would like to emphasise that those thanked do not necessarily subscribe to the analyses above or share any of the views expressed. I thank CERN for financial and other support during this work, which was also supported by a Royal Society University Research Fellowship and by the UK Particle Physics and Astronomy Research Council.

11 Note added July 2015 The previous arxiv versions and the published journal version of this article misstated the most conservative of BJSW’s implied bounds (i.e. those consistent with the highest probability of catastrophe), multiplying the probability by a factor of two. As well as correcting this transcription error, I have taken the opportunity to add ≈ symbols to the relevant figures in the paragraph stating BJSW’s various implied bounds. There are two reasons for this. First, BJSW’s calculations produce rounded rather than precise figures. Second, precisely which catastrophe risk bounds one derives from BJSW’s figures depends on precisely what sort of probabilistic reasoning one uses in considering the Moon’s survival or destruction as a result of cosmic ray impacts and the Earth’s survival or destruction as a result of the RHIC experiments. For example, should we derive risk bounds for RHIC in which we have 95% confidence, given that the Moon has survived? Or 99% confidence? Or should we use some other approach? BJSW offer no concrete proposal here. It should however be stressed that, whatever approach is used, this last point does not allow much scope for stretching the bounds. The stated risk bounds are derived from BJSW’s figures if one takes the probability of a dangerous strangelet to be such that the expected number created over the lifetime of the Moon is one, which implies a probability that the Moon survived to be (to very good approximation) e−1 =0.3678 .... So, the stated risk bounds are consistent with an appreciable probability of the Moon having survived. In other words, the survival of the Moon does not give any clear evidence against a catastrophe risk at the level of the stated bounds. If we believe we should reject hypotheses about strangelet creation only if they make the survival of the Moon seem pretty improbable, then the stated risk bounds are justified. Indeed, if we followed one standard method and rejected hypotheses about strangelet creation only if the Moon’s survival makes us at least (say) 95% confident that they are incorrect, we would justify even weaker bounds (consistent with still higher catastrophe risks). In any case, BJSW’s figures are consistent with a joint probability of both the Moon surviving to date and a hypothetical catastrophe at RHIC of e−1 times the stated catastrophe risk bounds. Since the probability of hypothetical catastrophe at RHIC is at least as large as this joint probability, it follows that (however one treats the separate events of Moon survival and hypothetical RHIC catastrophe) no catastrophe risk bound better than e−1 times the stated figures can be derived from BJSW’s calculations without introducing further assumptions that BJSW did not suggest in this part of their discussion. In particular, on BJSW’s most conservative assumptions, no risk bound better than 1 in 36788 can be derived. The omitted factor of 1/2 to BJSW’s most conservative implied risk bound probabilities makes no material difference to the arguments of this paper. Nor would a further factor of up to e−1 to any of BJSW’s implied risk bound probabilities do so. It is highly debatable whether any such factor should be included: to the best of my knowledge, no one has argued that it should. As noted above, one can as well argue that risk bounds should be derived by excluding only risk probabilities that make the Moon’s survival unlikely, in which case BJSW’s risk bounds should be higher rather than lower. In any case, given the magnitudes of the other relevant figures in the argument, the possibility of an extra factor of e−1 seems entirely moot. These corrections are made simply for the sake of accuracy. A further small correction is that the risk bounds quoted from BJSW [1,8] corresponding to their Cases I-III were previously listed in order of numerical size rather than in order of case number. To remove any possible −10 confusion, they are now listed above in case number order, so that for example the figures pcatastrophe <≈ 2 × 10 , −4 −5 pcatastrophe <≈ 10 , pcatastrophe <≈ 2 × 10 above correspond respectively to Case I, Case II, Case III of Ref [1]. I am very grateful to Eric Johnson for querying the previously stated figures and thus drawing my attention to the need for correction, and for several other very helpful comments and suggestions. Let me take the opportunity to add one other comment. As noted above, BJSW’s initial comments, characterising a risk of 1 in ≈ 10000 of destroying the Earth as “a comfortable margin of error” [1], are obviously inapplicable, and seem to reflect some surprising confusion on their part. Rereading their paper again prompted a guess at the nature of that confusion. BJSW’s arguments take the following form If there were a high probability (close to one) of strangelet-induced catastrophe at RHIC, then the expected number of dangerous strangelets produced by cosmic rays impacting the Moon over its lifetime would be very high (104 or higher). 4 Indeed, and it follows that the probability of the Moon having survived would be astronomically low (roughly e−10 or lower). This looks superficially enormously reassuring, given that the Moon has survived. The problem is that, to argue for the safety of RHIC, we need to exclude not just a high probability of hypothetical catastrophe but also a 4 small but significant probability of hypothetical catastrophe. It might seem that the number e−10 is so small that rescaling it by any significant probability will make no real difference. Unfortunately – and I wonder if this may be the point BJSW overlooked – the relevant rescaling is in the exponent. As noted above, on BJSW’s most conservative calculations, a probability of 10−4 of hypothetical catastrophe is consistent with a probability of e−1 of the Moon surviving.

12 [1] W. Busza et al., Review of Speculative ’Disaster Scenarios’ at RHIC, archived at www.arxiv.org/abs/hep-ph/9910333v1. [2] A. Dar et al., Will relativistic heavy ion colliders destroy our planet?, Phys. Lett. B, 470 142-148 (1999); archived at hep-ph/9910471. [3] E. Konopinski, C. Marvin and E. Teller, Ignition of the Atmosphere with Nuclear Bombs, Los Alamos Laboratory re- port LA-602. When the present paper was first drafted, this reference was archived and freely accessible at http://lib- www.lanl.gov/la-pubs/00329010.pdf. According to the Los Alamos National Laboratory library, access is presently not permitted, following a directive from the National Nuclear Security Administration. I assume this is a consequence of heightened security concerns since 11.9.01. [4] Pearl Buck, The bomb — the end of the world?, American Weekly, March 8, 1959, pp 8-11. [5] I am most grateful to Hans Bethe and Kurt Gottfried for this email correspondence. [6] P. Hut and M. Rees, How stable is our vacuum?, Nature 302, 508-509 (1983). [7] P. Hut, Is it safe to disturb the vacuum?, Nucl. Phys. A 418, 301c-311c (1984). [8] R. Jaffe et al., Review of Speculative ’Disaster Scenarios’ at RHIC, archived at www.arxiv.org/abs/hep-ph/9910333v2. Further minor alterations were made for the final published version: Rev. Mod. Phys. 72, 1125-1140 (2000), archived at www.arxiv.org/abs/hep-ph/9910333v3, [9] See for example Black Holes at Brookhaven?, letter to the Editors, Scientific American, July 1999, p.5; Big Bang machine could destroy Earth, article in The Sunday Times (London), 18.7.99, p.26. [10] Apocalypse Deferred, Scientific American, December 1999. [11] Black Hole Ate My Planet, New Scientist, 28 August 1999, pp. 24-27. [12] Committee Report on Speculative “Disaster Scenarios” at RHIC: synopsis, J. Marburger, 6.10.99. Archived for some while at http://www.bnl.gov/bnlweb/rhicreport.html. [13] S. Glashow and R. Wilson, Taking serious risks seriously, Nature 402, 596-597 (1999). [14] A. Kent, Problems with empirical bounds for strangelet production at RHIC, hep-ph/0009130. [15] Gambling with the Earth, New Scientist 7.10.00, p. 4. [16] Board Statement on Radiological Protection Objectives for the Land-based Disposal of Solid Radioactive Wastes, Documents of the NRPB 3, 3 (1992). Abstract available at http://www.nrpb.org.uk/Absd3-3.htm [17] C. Chapman and D. Morrison, Impacts on the Earth by asteroids and comets: assessing the hazard, Nature 367, 33-40 (1994). [18] F. Calogero, Might a laboratory experiment now being planned destroy planet Earth?, Interdisciplinary Science Reviews 25, 191-202 (2000).

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